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Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.
Circle packing has become an essential tool in origami design, as each appendage on an origami figure requires a circle of paper. [12] Robert J. Lang has used the mathematics of circle packing to develop computer programs that aid in the design of complex origami figures.
On a sheet of quadrille paper ("quad pad", e.g. Letter preprinted with a 1/4" square grid, or A4 with a 5 mm square grid), a freehand loop is drawn as the outer boundary of the racetrack. A large ellipse will do for a first game, but some irregularities are needed to make the game interesting.
This special graph paper is called a stereonet or Wulff net, after the Russian mineralogist George (Yuri Viktorovich) Wulff. [18] The Wulff net shown here is the stereographic projection of the grid of parallels and meridians of a hemisphere centred at a point on the equator (such as the Eastern or Western hemisphere of a planet).
Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation. In a similar way, an isometric view can be obtained in a 3D scene. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally (around the vertical axis) by ± ...
The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere. The counterparts of a circle in other dimensions can never be packed with complete efficiency in dimensions larger than one (in a one-dimensional universe, the circle analogue is just two points). That is ...
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